A Parliamentary petition signed by four million people demanding a second European Union referendum is the largest in history.
The British Parliament must consider debating any petition that reaches more than 100,000 signatures.
Tory backbencher Sarah Wollaston, an MP for Totnes, has said she doesn't' think "Trump should be invited to address both Houses of Parliament from Westminster Hall" on his visit, which will take place this year.
It took less than a day for the petition to receive 1.2 million signatures, ten times the amount required to earn an official response from the United Kingdom government.
Downing Street has declared that it will not entertain calls by the public to cancel U.S. President Donald Trump's proposed state visit to the United Kingdom despite a petition urging the government to do so having reached over a million signatures since Saturday.
The petition specifically cites Trump's misogyny and vulgarity, claiming it would "cause embarrassment to Her Majesty the Queen" were he to meet with the royal family.
Nationals of Iraq, Iran, Libya, Somalia, Sudan, Syria, Yemen, are affected by the ban, which includes those who are dual nationals of states other than the USA, and permanent U.S. residents.
Tens of thousands of Americans protested Trump's executive order around the country this weekend. "An invitation has been extended and accepted", a Number 10 spokesman added.
The petition against the visit, collecting 1.3 million votes by Monday mid-afternoon, was the second-most popular ever on the parliamentary website, after one calling for a second referendum on membership of the European Union drew more than four million signatures previous year.
The response follows Trump's executive order banning visitors, refugees, and migrants from seven majority-Muslim countries from entering the US.
But criticism of Ms May's wooing of Mr Trump erupted when - only hours after the prime minister had left the White House - the president signed an executive order suspending all travel to the USA of citizens of Iran, Iraq, Sudan, Somalia, Syria, Yemen and Libya for 90 days.
It said its position had not changed on the United States president's trip as Theresa May came under pressure to downgrade or axe the visit.
The order also bars all refugees entering the country for 120 days.